A general question: is it possible to retrieve information about how far away e.g. a computer is from a wifi-router. For instance I want to get data on my computer if I\'m 1
You can query the signal strength which is some kind of indication of distance and obstructions and a few other factors all rolled into one measure. With just plain wifi though this isn't possible directly.
I would recommend a measuring line or just good-old-fashioned guesstimating.
There is no "simple" way to do it (complex ways may involve building "accurate" signal maps ahead of time or trying to fit a better equation which is still subject to anumber of the limitations with the naive rule) and the rule of thumb "1/r^2" is just that -- a general rule of thumb. On the other hand, perhaps there is some existing software that will show you your RSS strength and make the task feel accomplished :-)
You will find useful links if you google for "RSS signal distance". This kind of task seems quite a common topic in academia w.r.t. small wireless devices ("motes") as well and there have been some interesting approaches to this problem such as the fitting of secondary low-frequency acoustic sensors.
Try measuring the response time of the router to pings, with the data rate set to constant to avoid that effecting the response time. Take lots of samples and remove outliers to reduce errors, but you will still have a substantial quantization error. Subtract the latency of the router and computer, divide by 6 then multiply by the speed of light and hopefully you will have the distance to a resolution of a few metres.